This morning I posted a writeup on how the 6.1 went when doing it tethered via USB to iTunes on a Mac and using a local (not iCloud) backup. Also mentioned that doing it this way left behind an extremely detailed log of the proceedings on the Mac.
Well, after perusing this thread again, then going back and examining my upgrade log, I think I have an idea why some of us have had equal or improved battery life in the first few hours post-upgrade, while others have seen the device drain away. The key, it would seem, is the kind of backup you have: iCloud vs. local.
You see, the upgrade wipes the phone absolutely clean. A Restore is mandatory after completion, else you'd have a totally blank phone and all users would be screaming bloody murder. Where it gets the stuff for the restore causes the battery longevity issues.
When using a local storage, EVERYTHING on the phone gets saved. Every little bit. So Restore is merely an act of copying all back, at USB speed. Furthermore, iTunes tells you to wait till the phone comes back online (post-Restore) before unplugging it. All this is supported by the log I got as a bonus.
When I was reviewing what iCloud storage offered, they clearly state that only "the most important data" is placed in the cloud. Naturally, Apple will only give us the bare minimum to store only irreplaceable data. Stuff that can be recomputed, like thumbnails, indexes, etc., are left out. So, when you upgraded OTA only the barebones data went in the cloud, and then fetched back at the end. THEN the phone had to chug along for quite awhile to reconstruct the rest of the stuff. The bigger the photo collection, the larger the song lists, the longer the contacts, the more the phone had to do. And there goes the battery.
Maybe someone who hasn't upgraded and plans to do so OTA can make sure to have an app like Device Doctor installed, where you can measure CPU workload and the number of processes. Check it before the upgrade and immediately after to confirm whether the phone is chugging away like a maniac or not.